On Ricci tensors of Randers metrics

In this paper, we study Randers metrics and find a condition on the Ricci tensors of these metrics for being Berwaldian. This generalizes Shen’s Theorem which says that every R-flat complete Randers metric is locally Minkowskian. Then we find a necessary and sufficient condition on the Ricci tensors under which a Randers metric of scalar flag curvature is of zero flag curvature.